If \(A\cup B=A\), which conclusion is correct?
Answer and explanation
Correct answer: \(B\subseteq A\)
The union \(A\cup B\) contains all elements of A and all elements of B. If the union is equal to A, then B cannot contain any element outside A; otherwise that element would appear in the union and make it larger than A. Hence every element of B belongs to A, which means \(B\subseteq A\). The other choices are not necessary and may contradict this containment.
Frequently asked questions
What is the correct answer to this question?
\(B\subseteq A\)
Why is this the correct answer?
The union \(A\cup B\) contains all elements of A and all elements of B. If the union is equal to A, then B cannot contain any element outside A; otherwise that element would appear in the union and make it larger than A. Hence every element of B belongs to A, which means \(B\subseteq A\). The other choices are not necessary and may contradict this containment.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
